Anna Jessen December 13, 2016 Final Draft Transit Subsidies and their Effect on Ridership and Optimal Transit Supply Introduction As populations grow and traffic congestion worsens in urban areas, there is arguably a need for more mass transit. Perhaps one of the biggest obstacles for increasing mass transit is the high fixed costs associated with the operation of the various modes of mass transit. Transportation subsidies for passengers account for much of the high public expenditures related to public transit. In most agencies, passenger fares for public transportation are heavily subsidized (Parry and Small 2009, 700). An analysis of the 20 largest transit systems in the United States reveals that bus subsidies (measured by the difference between operating costs and passenger fare revenues) range between 57 and 89 percent of operating costs (Parry and Small 2009, 700). One purpose for such high subsidies is lower transit fares discourage automobile use, which translates into reduced external costs from traffic congestion, air pollution, and accidents (Parry and Small 2009, 700). This capstone will analyze welfare maximization from the transit planner’s perspective using a theoretical model. The theoretical model aims to maximize social welfare with respect to the number of trips demanded as well as the number of buses in order to inform decisions surrounding optimal transit supply. The authors of one utility maximizing study discovered that high subsidies are justified and that increasing the subsidy is welfare improving even while current subsidy levels are often over fifty percent (Parry and Small 2009, 717). This capstone also intends to analyze how changes in fare subsidies affect ridership. To help answer this question, an empirical investigation across agencies will be performed. The analysis will focus
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Anna Jessen
December 13, 2016
Final Draft
Transit Subsidies and their Effect on Ridership and Optimal Transit Supply
Introduction
As populations grow and traffic congestion worsens in urban areas, there is arguably a
need for more mass transit. Perhaps one of the biggest obstacles for increasing mass transit is the
high fixed costs associated with the operation of the various modes of mass transit.
Transportation subsidies for passengers account for much of the high public expenditures related
to public transit. In most agencies, passenger fares for public transportation are heavily
subsidized (Parry and Small 2009, 700). An analysis of the 20 largest transit systems in the
United States reveals that bus subsidies (measured by the difference between operating costs and
passenger fare revenues) range between 57 and 89 percent of operating costs (Parry and Small
2009, 700). One purpose for such high subsidies is lower transit fares discourage automobile use,
which translates into reduced external costs from traffic congestion, air pollution, and accidents
(Parry and Small 2009, 700).
This capstone will analyze welfare maximization from the transit planner’s perspective
using a theoretical model. The theoretical model aims to maximize social welfare with respect to
the number of trips demanded as well as the number of buses in order to inform decisions
surrounding optimal transit supply. The authors of one utility maximizing study discovered that
high subsidies are justified and that increasing the subsidy is welfare improving even while
current subsidy levels are often over fifty percent (Parry and Small 2009, 717). This capstone
also intends to analyze how changes in fare subsidies affect ridership. To help answer this
question, an empirical investigation across agencies will be performed. The analysis will focus
on panel data from 1992 to 2014 for agencies that operate in large urbanized areas (population
greater than one million) that utilize all modes of transportation.
Zhou, H.S. Kim, Schonfeld and E. Kim (2008) analyzed the subsidies associated with
both flexible route bus systems and fixed route bus systems. A fixed route system involves
predetermined stops on a fixed schedule while a flexible system is sometimes known as an on-
demand system. They found that for a wide range of subsidy values for a fixed route bus system,
the net effect of producer and consumer surplus produced a rather flat optimal welfare curve
(Zhou et al. 2008, 659). This presents a different viewpoint than the paper by Parry and Small. In
2001, Schmidt specifically analyzed federal transit subsidies and concluded that even though an
output subsidy increased the amount of buses a transit authority provides, the subsidy did not
really incentivize riders to use the additional service (Schmidt 2001, 255). Subsidies play a
significant role in how mass transit is funded but are those seemingly high subsidies worth it?
The purpose of this paper is to analyze which variables impact welfare optimization as well as to
analyze the effect of subsidies on ridership.
Literature Review
Extensive scholarly research has been completed that can inform transit subsidy analysis.
This literature review centers on four major themes. One major reason for the promotion of
public transit is based on an externality argument. For example, mass transit promotes private
investment. Second, when consumers choose mass transit instead of private transit, there is a
reduction in the negative externalities associated with automobiles. Past research on subsidies in
general has revealed a few cases where a subsidy has caused both negative and unintended
consequences. In a transit context, subsidies are revealed to be welfare improving. Also, transit
subsidies play a role in user demand for transit by affecting prices. Additionally, planners must
decide the subsidy level as well as the amount of transit to provide. On a broader scale, when
consumers are uncertain of the quality of the good, they look at signals of quality to determine
their willingness to pay. This is relevant for transit because there is an element of uncertainty
surrounding reliability. Analyzing these themes will assist in an analysis of a subsidy’s effect on
ridership.
Positive and Negative Transit Externalities
The majority of funding for state highway projects comes from taxes, federal highway
grants, and the general fund (Nesbit and Kreft 2009, 94). Not only does public investment in
transportation infrastructure support the movement of goods and people, it also has the
opportunity to affect private investment as well. The Northeast United States is home to a mature
transportation system and is the subject of a study completed by Chen and Haynes in 2015. This
study found highway infrastructure to have a positive effect on regional economic output (Chen
and Haynes 2015, 10). Additionally, the authors found public rail to have a significant positive
impact on regional output, but highways still have a larger positive impact overall. However,
public transit has a relatively smaller effect on regional output as compared to highway and
public rail (Chen and Haynes 2015, 11). Overall, highway infrastructure has the largest influence
followed by public rail, public airport, and public transit. (Chen and Haynes 2015, 12). In terms
of public transit, it has a rather small effect on output even though it receives a relatively high
level of public investment. Passenger rail, for example, functions as a complement to other forms
of transportation. Pereira and Andraz (2005) discovered similar conclusions in their study of
Portugal’s less mature infrastructure from 1976 to 1978. They concluded that public investment
in infrastructure crowds in private investment and employment (Pereira and Andraz 2005, 194).
Additionally, infrastructure investment has improved labor productivity and promoted long-term
growth (Pereira and Andraz 2005, 194). The largest effect on output comes from investment in
ports followed by roads, airports and railroads. (Pereira and Andraz 2005, 194).
Automobiles are known to cause negative externalities including air pollution, oil
dependency, traffic congestion, traffic accidents, noise, and urban sprawl (Parry, Walls, and
Harrington 2007). Automobiles emit carbon monoxide into the atmosphere, which can cause
breathing difficulty and cardiovascular problems (Parry, Walls, and Harrington 2007, 374). In
one study about Belgian transportation, the authors found that more than 90% of the external
costs related to road accidents, air pollution, noise and land use come from private passenger
transportation (Lesceu 1993, 474). More than half of the external costs from transportation arise
from traffic accidents and are then followed by cost of land use and cost of air pollution (Lesceu
1993, 474). Negative externalities are an issue because others have to bear these costs. Lesceu
writes, “Consequently, the negative side-effects of transportation are not charged to the users of
transportation services. There is a discrepancy between the private expenses of the user and the
external costs borne by all members of society” (Lesceu 1993, 463). She mentions that market
theory suggests a more rational use of natural resources can be obtained by internalizing the
external costs of transportation services (Lesceu 1993, 475). Additionally, reducing
transportation pollution and the external costs associated with it can be achieved by reducing
vehicle miles traveled (Parry, Walls, and Harrington 2007, 375).
One purpose for public transportation investment is to reduce these negative automobile
externalities. In a study focused on Aragon, Spain, the authors found that travelling by bus or
train resulted in an individual cost savings of 75% and 88% respectively compared to using a
private automobile (Duarte et al. 2014, 420). This study also found if households choose public
transportation over private, there will be a significant reduction in harmful emissions as a result
Commented [TKM1]: This paragraph is very well written!
of lower fuel consumption (Duarte et al. 2014, 424). Lenzen and Dey (2002) reached similar
conclusions. In Australia, road vehicles consume 75% of all transport energy and more than 80%
of that is the result of private cars (Lenzen and Dey 2002, 389). Shifting away from private cars
and choosing to travel on public transportation can potentially reduce greenhouse gas emissions.
Additionally, this will increase employment and income (Lenzen and Dey 2002, 394). In the
scenario where spending on public transportation is increased to discourage private car use,
Duarte et al. (2014, 427) found a reduction in the consumption of refined petroleum products.
Overall, the authors conclude policies to promote household changes in transportation
consumption may have positive environmental impacts without affecting other economic
variables (Duarte et al. 2014, 427).
Unintended Consequences of a Subsidy
Subsidies are usually put in place to encourage consumption of a good but sometimes
there are unintended consequences. As Just and Hanks (2015, 1397) note, an emotional response
to a policy may cause different results than a traditional analysis would predict. If there is an
emotional attachment to a good, then consuming that good brings either enjoyment or
dissatisfaction. If a policy reinforces this emotional attachment then the emotion will be felt to a
greater extent. (Just and Hanks 2015, 1390). For example if a parent is provided with a subsidy
for child healthcare, they might feel more enjoyment because the subsidy reinforced healthcare,
which is seen as a positive good (Just and Hanks 2015, 1390). Similarly, Gneezy, Meier, and
Rey-Biel (2011, 206) discuss the role of intrinsic motivations when analyzing the effectiveness
of an incentive. The effect of a subsidy, a type of incentive, will depend on its relationship to
intrinsic motivation. Just and Hanks (2015, 1386) suggest policies that are more empathetic to
consumer emotions will improve market welfare more than combative or confrontational
policies. An example of a combative policy would be one that threatens individual freedom, such
as mandatory vaccinations. A subsidy that is more empathetic to consumers is likely to be a more
effective policy (Just and Hanks 2015, 1398).
Unintended effects of a subsidy appear in both consumption and production subsidies. A
study about the effect of food price subsidies on nutrition for poor households in China found no
measurable effect on nutrition and may have actually reduced caloric intake in one province
(Jensen and Miller 2011, 1221). In the Hunan province, the subsidies induced substitution away
from the subsidized staple food toward other foods with non-nutritional attributes (Jensen and
Miller 2011, 1221). The authors note this result is consistent with Giffen behavior (Jensen and
Miller 2011, 1219). Even though the subsidies did not improve nutrition, they did improve
welfare. The findings of this study are driven by the wealth effect of the price change (Jensen
and Miller 2011, 1221). The subsidies freed up income that consumers chose to spend on other,
perhaps tastier but less nutritious, foods (Jensen and Miller 2011, 1222). The consumption of less
nutritious foods is seen as a negative outcome. This nutrition study shows a negative unintended
effect of a consumer price subsidy, but unintended effects can also be observed for production
subsidies such as clean energy subsidies. The authors discovered that a subsidy promoting the
production of low carbon energy actually found the subsidy to have a perverse effect
(Hutchinson, Kennedy, and Martine 2010, 6). The subsidy did cause a shift toward cleaner
energy production, but at the same time caused an increase in energy consumption because the
subsidy caused the equilibrium price of energy to fall (Hutchinson, Kennedy, and Martinez 2010,
6). Even though clean energy production increased, however, due to increased consumption of
energy overall, the authors found the subsidy resulted in an increase in carbon emissions
(Hutchinson, Kennedy, and Martinez 2010, 6). This increase in carbon emissions is an example
of how a production subsidy can result in an unintended consequence with potentially negative
implications.
Transit Subsidies--Welfare
Improvements in welfare are another commonly cited reason for transit subsidies.
Numerous articles point to estimating welfare as a way to determine optimal subsidy levels. In a
2009 study specifically about transit systems in Washington, D.C., Los Angeles, and London, the
authors found increasing the subsidy beyond fifty percent for all modes, periods, and cities to be
welfare improving in all but one case (Parry and Small 2009, 717). They note the majority of
welfare gains came from reducing road congestion (Parry and Small 2009, 717). In a 1997 study
about transit in Chicago, the authors explain increasing fare subsidies has a greater overall
benefit to society than increasing bus service levels (Savage and Schupp 1997, 111). The authors
suggest cutting service levels in order to lower fares is welfare improving. They also note the
transit authority has tried to maintain bus frequency even during falling demand, and this has
caused the transit authority to raise fares. Instead of fare increases that hurt welfare, they suggest
decreasing service levels (Savage and Schupp 1997, 111-113). This will also result in an increase
in consumer surplus. Zhou et al. (2008) found that as the subsidy increases for fixed route bus
systems, where routes and stops are fixed, welfare also increases. This is shown as an increase in
consumer surplus, but it is coupled with a decrease in producer surplus. The net effect is a rather
flat optimal welfare curve over a range of subsidies. These authors recommend that welfare
optimization should not be pursued to its absolute maximum for that reason (Zhou et al. 2008,
651-652). This would result in a relatively small decrease in welfare, but the budget deficit
would be zero.
Transit Subsidies—User Demand
More than one study has found passenger sensitivity to the level of service: the number of
scheduled miles in the transit system. In a study about transit in El Paso, the authors note riders
are more sensitive to changes in the level of service than to changes in fare in the short run. Their
analysis found increasing vehicle revenue miles1 per month results in increased ridership
(Fullerton and Walke 2013, 3928). Transit demand in Chicago is also more sensitive to bus
frequency than to fares (Savage and Schupp 1997, 112). In Chicago, demand is inelastic with
respect to service frequency, but the author notes the cost of increasing buses on existing routes
would be too high (Schupp 1997, 112).
Other factors also determine transit demand and ridership such as car ownership, gas
prices, and economic conditions. In the same study about El Paso, the authors mention increases
in car ownership tend to lower ridership. At the same time, increases in gasoline prices can
encourage consumers to ride public transport instead of taking a private car (Fullerton and Walke
2013, 3930). Additionally, the study discovered an increase in positive economic conditions in
Mexico is connected to an increase in transit ridership (Fullerton and Walke 2013, 3930). In the
study by Parry and Small (2009, 717), they found fares to have an effect on ridership. They
found when fares are adjusted to optimal levels (in terms of total welfare), ridership decreased in
Los Angeles while it increased in London.
Transit Subsidies—Planner’s Decisions
One decision transit planners face is the decision about the level of the subsidy.
Depending on the focus of the study, different conclusions are drawn about optimal subsidy
levels. Parry and Small (2009, 717) found the current large subsidies in Los Angeles,
Washington, D.C., and London to be justified. They discovered the optimal fare subsidies to be
1 The number of scheduled miles for vehicles in revenue service
more than two thirds of average operating costs in eleven out of twelve cases (Parry and Small
2009, 717). Tisato (1997, 342) focused on user economies of scale for buses in Adelaide and the
authors found subsidy levels are higher than can be justified. The author does not, however,
advocate for a zero subsidy. He acknowledges the optimal subsidy still exceeds $40 million in
most cases. In a different study by Zhou et al. (2008, 659), the authors found the effect of a
subsidy on welfare was different for fixed route and flexible route bus systems. A fixed route
system is the most familiar type of bus service where buses follow fixed routes on a fixed
schedule. On the other hand, a flexible system operates more like an on demand service where
people request rides. For a fixed route bus system, they suggest a low transit subsidy policy;
however, that policy is less preferable for a flexible route system.
Another decision transit planners face is the amount of transit routes and frequency to
provide. One reason federal mass transit operating subsidies exist is to encourage transit agencies
to increase their service. A 2001 study that analyzed data from the mid-1990s concluded these
subsidies have increased bus output by six to eight percent per year as compared to output
without the subsidy (Schmidt 2001, 255). Schmidt (2001, 256) claims these subsidies
specifically incentivize increasing output regardless of demand and do not actually incentivize
increasing ridership. Federal transit subsidies with the intent to increase transit supply only
increase output to a certain extent. As transit output increases, marginal costs also increases, so
there is a natural limit to how much output can be increased through subsidies that are limited
(Schmidt 2001, 255). Sakano et al (1997,121) examined the impact of increasing output without
regard for demand and found federal subsidies create allocative inefficiencies. Since operating
subsidies are used to cover losses, transit agencies do not have an incentive to reduce labor and
fuel costs (Sakano, Obeng, and Azam 1997, 121). The authors suggest using subsidies to
incentivize firms to operate efficiently. They argue firms should only get subsidies if they are
facing a loss after making every effort to operate efficiently by reducing costs (Sakano, Obeng,
and Azam 1997, 121).
Demand with Uncertain Quality
Buyers use signals to help determine willingness to pay when the quality of a good is
unknown. Oftentimes, consumers can observe price before purchasing a product and can only
perfectly observe the quality of the product after the purchase. However, quality signals exist
prior to the purchase of that product. In the case of high prices, consumers associate high quality
with the product (Hey and McKenna 1981, 64). For example, in the cherry market, some sellers
sort cherries based on their size while other sellers don’t sort by size. It turns out buyers pay a
higher price for cherries from non-sorting firms. Over time, buyers have discovered through
experience, reputation, and other signals, that cherries from non-sorting firms are of higher
quality (Rosenman and Wilson 1991, 656). This occurs even though buyers cannot observe
differences in quality among cherry sellers of a certain standard (Rosenman and Wilson 1991,
658). The signal of quality in the cherry market is the firm’s sorting behavior and buyers are
willing to pay more for cherries they perceive to have a higher quality. In the cherry market,
higher quality is associated with a higher price.
Coins sold in online auctions on e-bay rely on quality signals similar to transit agencies.
Since a buyer is unable to directly observe the quality of the coin before purchasing, they need to
rely on quality signals to inform their willingness to pay. Melnik and Alm (2005, 326-327) found
a seller’s reputation has a positive and statistically significant impact on the consumer’s
willingness to pay. A better reputation signals a higher quality of good. Additionally, complaints
about the seller have a negative impact on willingness to pay (Melnik and Alm 2005, 327).
Essentially, buyers use the reputation of the seller as a signal of the good’s quality. A perceived
higher quality leads to a higher willingness to pay. Similarly, Ma, Ferreira, and Mesbah (2013,
13) recognize improving transit service reliability is the most cost-effective approach to
encouraging increased transit use. Longer wait times and longer traveling time suggest
unreliability. Here, transit reliability, a signal of quality, impacts the reputation of the transit
agency. Additionally, Van Vugt, Van Lange, and Meertens (1996, 384), acknowledge public
transportation can compete with private cars when public transportation provided shorter average
travel time and equally reliable travel time. Again, reliability, one way to measure quality,
impacts a rider’s decision to use public transportation. Demand in online auctions and for public
transit both rely on perceived quality.
Theoretical Model
To assist in the analysis of public transport subsidies, a theoretical model can be used to
help identify the optimal supply of public transportation. A working paper written by Nilsson,
Ahlberg and Pyddoke (2014) analyzes the relationship between subsidies and optimal transit
supply. One element of the model presented in this paper is particularly relevant to this capstone.
Specifically, the authors examine the use of vouchers in a public transportation monopoly.
Essentially, under a voucher system, both the passengers and the supply of bus trips are
subsidized. Each passenger is charged a fare while at the same time the public sector provides a
voucher for each trip to cover the remaining cost. The authors are interested in maximizing
welfare in the bus system by choosing the quality (number of buses to operate) and the fare to
charge.
In this model, a couple assumptions are made. Perhaps the most basic assumption is that
the regional public sector body has decided a bus service should be operated. It is assumed that
all decisions about bus supply are made with full information. For example, information
regarding demand, costs, production costs, as well as any other information about the conditions
the buses will be operated under is known. The authors assume the inverted demand function is
concave in the number of trips and the number of buses. This means demand is nonlinear and
increasingly responsive to changes in price. In terms of the cost function, it is assumed to be
convex for producing a number of trips given a certain quality. For this model, there is a
monopoly where only one bus operator exists. The following table (Table 1) shows the
definitions of variables included in the model.
Table 1: Variable Definitions
Variable Definition
𝜋 Profits
x Demand for trips (quantity)
b Service quality (number of buses)
p Price (or fare)
c Cost
𝑠𝑚𝑥 Subsidy targeting number of trips. m is
optimal subsidy under monopoly
𝑠𝑚𝑏 Subsidy targeting number of buses. m is
optimal subsidy under monopoly
w welfare
𝜀 Price elasticity of demand for trips
The overall objective of the model is to maximize social welfare with respect to x (trips)
and b (service quality). Equation 1 relates welfare to the price or fare that is charged to riders per
trip. Essentially, equation 1 represents revenue minus cost where revenue is found by integrating
over the range of all users, or 𝜈.
𝑚𝑎𝑥 𝑊 (𝑥, 𝑏) = ∫ 𝑝(𝑣, 𝑏)𝑑𝑣 − 𝑐(𝑥, 𝑏)𝑥
0
(1)
The first marginal condition (equation 2a) is found by taking the first partial derivative of
equation 1 with respect to x, the number of trips. This equation serves the purpose of setting
price equal to marginal cost given b (service quality). It also shows how price responds to the
number of buses chosen (service quality).
𝜕𝑤
𝜕𝑥= 𝑝(𝑥, 𝑏) −
𝜕𝑐
𝜕𝑥(𝑥, 𝑏) = 0 𝑝 =
𝜕𝑐
𝜕𝑏(𝑥, 𝑏) (2𝑎)
The other marginal condition (equation 2b) is found by taking the first partial derivative
of equation 1 with respect to b, service quality. Here, as the number of buses change, consumers
will respond with a change in demand.
𝜕𝑤
𝜕𝑏= ∫
𝜕𝑝
𝜕𝑏
𝑥𝑤
0
(𝑣, 𝑏)𝑑𝑣 −𝜕𝑐
𝜕𝑏(𝑥, 𝑏) = 0 (2𝑏)
With the welfare maximization objective established such that essentially, price must
equal marginal cost with respect to service quality (2a) and marginal cost with respect to changes
in quality must equal the effect of price responsiveness of consumers with respect to quality, it is
now applied to a bus system operator who is a monopolist and uses vouchers under complete
information. Under a voucher system, for each passenger trip, the operator receives a fare from
the passenger and some amount from the government to make up for the costs the fare does not
cover. Additionally, in this model, the operator receives a voucher (also known as a subsidy) for
each bus that is operated. Equation 3 is the bus operator’s objective function. The operator wants
to maximize profit with respect to x (number of trips) and maximize profit with respect to b
(service quality).
𝜋(𝑥, 𝑏) = 𝑝(𝑥, 𝑏)𝑥 + 𝑠𝑚𝑥 𝑥 + 𝑠𝑚
𝑏 𝑏 − 𝑐(𝑥, 𝑏) (3)
The following equations, equations 4a and 4b, represent the marginal conditions. The left
side of equation 4a represents how profits change as the number of trips changes. With each
additional trip, the agency receives p, which is the fare. The next part of the equation, 𝜕𝑝
𝜕𝑥𝑥 ,
represents how if the number of trips is changed, then the price will probably also have to
change, which will impact revenue. For example, if the price is dropped, it is likely the number
of trips taken will increase so the agency will receive revenue from a greater number of trips.
Even though the price has dropped, the subsidy targeting the number of riders, 𝑠𝑚𝑥 , will make up
for some of that lost revenue due to the lower price. The first three terms in the equation rise as
the number of trips increases because the marginal revenue changes as the number of trips
changes. The last term, −𝜕𝑐
𝜕𝑥 , represents marginal cost. Essentially, equation 4a says if the
correct number of trips is chosen, then marginal revenue will equal marginal cost. Equation 4b is
very similar but instead describes how profit changes as the quality changes. The purpose of this
equation is to show that ridership might change if quality is improved.
𝜕𝜋
𝜕𝑥= 𝑝 +
𝜕𝑝
𝜕𝑥𝑥 + 𝑠𝑚
𝑥 −𝜕𝑐
𝜕𝑥= 0 (4𝑎)
𝜕𝜋
𝜕𝑏=
𝜕𝑝
𝜕𝑏𝑥 + 𝑠𝑚
𝑏 −𝜕𝑐
𝜕𝑏= 0 (4𝑏)
These marginal conditions are then combined with the marginal conditions from the
welfare maximization for the transit authority (equations 2a and 2b) in order to make the
monopolist abide by the conditions of the transit authority’s welfare maximization. Here, 𝜀𝑥 ≡
𝜕𝑥
𝜕𝑝
𝑝
𝑥< 0 is the price elasticity of demand for trips. Solving the above equations for 𝑠𝑚
𝑥 and 𝑠𝑚𝑏
results in the following equations (5a and 5b) for the specification of the optimal subsidies for
the transit authority to choose. The first condition (5a) represents the necessary subsidy level to
induce the operator to charge passengers a welfare maximizing price given a certain amount of
buses.
𝑠𝑚𝑥 = −
𝜕𝑝
𝜕𝑥𝑥𝑤 =
𝑝𝑤
𝜀𝑥 (5𝑎)
𝑠𝑚𝑏 = ∫
𝜕𝑝
𝜕𝑏𝑑𝑣 −
𝜕𝑝
𝜕𝑏𝑥𝑤
𝑥𝑤
0
(5𝑏)
The optimal passenger subsidy, 𝑠𝑚𝑥 , that is chosen is related to the price elasticity of
demand for trips. The following shows that price elasticity for trips helps determine whether the
optimal passenger subsidy is lower, equal to, or higher than the welfare maximizing price.
Basically, the subsidy will be higher with a higher price elasticity for trips.
𝑠𝑚𝑥 [
> 𝑝𝑤 𝑖𝑓 𝜀𝑥 > −1
= 𝑝𝑤 𝑖𝑓 𝜀𝑥 = −1
< 𝑝𝑤 𝑖𝑓 𝜀𝑥 < −1 (6)
The solid curve in Figure 1 represents demand for bus service. The dashed line
represents marginal revenue after the introduction of the subsidy. The dotted line represents
marginal revenue for a monopolist before the introduction of subsidies. The horizontal line
represents both price and the marginal cost of bus service. The figure shows that once the
subsidy is added, the marginal revenue line shifts up.
Figure 1: Demand, Marginal Cost, and Revenue of Bus Service Under Monopoly
Overall, a voucher approach for subsidizing bus transit requires taxpayer funds but the
benefit of a voucher system is the flexibility it provides. This type of system is able to adapt to
changes in supply and demand. Under a voucher system, the transit authority receives some
amount, or voucher, for every trip taken by a passenger in addition to the fare paid by the
passenger, but the voucher does not cover the full cost of the ride. The transit authority still has
discretion over what fare to charge (while keeping demand in mind), but the government
determines the value of the voucher received for each ride. Here, the transit authority maintains
flexibility over the fare to charge. Secondly, the transit authority also receives a voucher for each
bus provided. They also maintain flexibility over the number of buses to run but the government
determines the value of the subsidy for the quantity of buses.
The authors found in their analysis no evidence that vouchers would be hazardous to the
market’s performance (Nilsson, Ahlberg and Pyddoke, 2014, 26). In contrast, in a completely
unregulated public transportation market, issues with inefficiency, safety hazards, and conflict
between operators and lack of price competition arise. These examples do not arise under a
Price
Quantity- Bus Service
voucher system. In order for the voucher system to work, the vouchers would need to be linked
to the number of passengers as well as to the number of vehicles the operator chooses to use.
With social welfare maximization as the goal, it is important to subsidize both the supply and
demand sides. On the demand side, the subsidy corrects the price to encourage ridership and
welfare maximization. On the supply side, the subsidy encourages the optimal supply of buses
and welfare maximization. Both of these elements work together to achieve total maximum
welfare.
It is important for public transportation planners and operators to find the optimal subsidy
in order to maximize welfare, maximize profit, and encourage ridership. In this model, the
planners are able to choose the number of buses to run and have some flexibility in the level of
fare to set, while keeping an eye on demand. When trying to find the optimal subsidy, many
factors have to be taken into account. This model demonstrates the tradeoffs and incentives
involved when determining a subsidy level when the number of buses and the number of trips are
the parameters. A change in the subsidy level will result in a change in profit for the monopolist
operator. It also recognizes that any change in the subsidy (which affects the fare) will result in
changes in ridership. Using a model such as this one can help a transit planner predict how well
their chosen subsidy level and bus supply level obtain the goal of welfare maximization and
profit maximization.
The theoretical model shows the optimal supply of transit relies both on maximizing
welfare and maximizing profit. The demand for trips as well as the quality of service play a role
in this maximization. It is important to take the demand side into account in order to optimize
supply and factors such as reliability (service quality) are essential to this model. For these
reasons, variables impacting demand are included in the following empirical model. The
empirical analysis also focuses on transit subsidies. Instead of a voucher system, the transit
authority receives funding subsidies from the government whose value does not necessarily
depend on the number of trips.
Empirical Analysis
The econometric portion of this paper analyzes how a change in the subsidy level affects
ridership. Ridership, or the demand for bus service in the model above, plays a role in welfare
maximization and profit maximization. Price elasticity with respect to trips, as also mentioned
above, influences how the subsidy level is chosen. Since increasing ridership on public
transportation is also one of the goals of the planner, it is necessary to analyze whether a change
in the fare (via the subsidy) is a viable solution by empirically estimating the relationship
between the subsidy levels chosen by planners and the corresponding ridership that results.
I. Data
The main data for this analysis comes from the U.S. Department of Transportation
National Transit Database. The fifty largest metro areas in the United States are included in the
analysis with the exception of a few. Puerto Rico was removed because it is not located in the
United States even though it is included in the National Transit Database. Austin, Texas, New
Orleans, Louisiana, and Las Vegas, Nevada were excluded due to insufficient data. Each metro
area is identified by a UZA2 number and each UZA contains multiple cities and transit agencies.
For example, Everett Transit is included in UZA 14, which is considered the Seattle metro area.
All modes of transportation from bus to various types of rail were included, due to the difficulty
of extracting individual modes from the data. Even smaller forms of transportation like cable
2 UZA stands for Urbanized Area
cars and ferries were included where applicable. The panel data used in this analysis is from
1992 until 2014.
The dependent variable is abbreviated UPT, which is defined as unlinked passenger trips.
Every time a passenger boards a public transportation vehicle, it is counted as an unlinked
passenger trip. In other words, a transfer from a train to a bus would count as two trips instead of
one. This variable is used to measure ridership. In order to obtain one ridership data point per
UZA, all of the unlinked passenger trips for each mode of transportation across all agencies in
the UZA were summed.
The variable subsidy was calculated using fare revenue data and funding data from the
National Transit Database because explicit subsidy numbers are not available. Essentially, fare
revenue only covers a certain amount of the funding that is needed to run the agency, and it is
assumed that a subsidy covers the rest. The subsidy variable represents the percent of funding
that is not covered by fare revenue. The total funding figures across all modes of transportation
across all agencies in the UZA were summed. Fare revenue figures across all modes of
transportation across all agencies in the UZA were also summed. To calculate subsidy, the
formula (1—(fare/funding)) was performed for each UZA. For example, if King County Metro
fare revenue accounts for 30% of their total funding then it is assumed there is a 70% subsidy.
The variable fleet age was calculated using active fleet data and average age of fleet for
each transit authority within a UZA. Only bus fleet data from active authorities was used in the
calculation. A weighted average was used so that transit agencies with a larger fleet would
proportionally influence the average age. This variable is used as an indicator of reliability and is
based on the assumption that older fleets are more likely to break down. The variables included
in the econometric model are found in Table 2.
Table 2: Variable Definitions and Sources
Variable Variable Definition Source
UPT Unlinked passenger trips.
Used to measure ridership
USDOT National Transit Database
UZA population Population of each
urbanized area (UZA)
Bureau of Economic Analysis
Fleet age Weighted average bus age
for the urbanized area using
active fleet data and average
age of fleet for each transit
authority within the UZA
USDOT National Transit Database
Hours of delay Annual hours of delay per
auto commuter. Used as a
measure of roadway
congestion.
Texas A&M Transportation Institute
Subsidy Calculated using the
formula 1—(fare/ funding)
USDOT National Transit Database
Gasoline cost in 2014
dollars
Average state gasoline cost
in dollars per gallon for the
year. Adjusted for inflation
Texas A&M Transportation
Database using CPI from The
Federal Reserve Bank of St. Louis
Income in 2014 dollars Annual per capita personal
income for each urbanized
area adjusted for inflation
Bureau of Economic Analysis using
CPI from The Federal Reserve Bank
of St. Louis
Table 3 includes descriptive statistics for the given variables. The minimum unlinked
passenger trips is zero because Virginia Beach reported zero trips from 1992 to 1999. This is
likely due to a merger between agencies. Virginia Beach was kept in the data set because the rest
of their data was complete. Unlinked passenger trips has a very high standard deviation because
trips range all the way from zero to over four billion trips in New York. In terms of income, the
minimum is associated with Cleveland in 1993 and the largest is associated with Bridgeport-
Stamford in 2007. UZA population has a rather high standard deviation at 3,224,752 people
because the population data ranges from a minimum of 588,751 people to a maximum of just
over 20 million people in New York. The nine largest UZAs in 2014 all contained over five
million people. Additionally, many of the cities included in this analysis have seen their
populations increase since 1992. The mean of the weighted average fleet age for the sample is
7.36 years and has a relatively small standard deviation of 1.8 years. The maximum weighted
average fleet age is 15.3 years. This indicates the majority of the agencies in the sample are using
relatively up to date fleets. This does not mean all transit vehicles are new, it just indicates most
agencies are trying not to let their fleets age substantially. The mean subsidy in this sample is
75% and the minimum subsidy is 41%. This indicates all cities in the sample rely on a sizable
subsidy. Interestingly, the maximum subsidy is 99% which occurred in Phoenix in 1993 (it has